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lfunc_lfunctions • Show schema
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{'Lhash': '2936402735009434353161054740141', 'a10': [0.0890756181890956, -0.7189813863588355], 'a2': [1.1952154259715277, -0.7559497903430487], 'a3': [0.881921264348355, 0.47139673682599764], 'a4': [0.8570798289606015, -1.8070457013559083], 'a5': [0.3249891906080366, -0.3960004745338755], 'a6': [1.4104381640134778, -0.10326754327614242], 'a7': [-2.624989042279641, -1.7539616028234954], 'a8': [-0.3416407862175566, -2.8077182147061426], 'a9': [0.5555702330196022, 0.8314696123025452], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.1952154259715277, 0.7559497903430487]]], [3, [[1.0, 0], [-0.881921264348355, -0.47139673682599764]]]], 'bad_primes': [2, 3], 'central_character': '384.109', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '1872915563433540188476428178252', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.3527765154769011, 'root_number': '0.4462013620894713 + 0.8949325921372517*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.176388257738', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.31641331963299723725309191666', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.42269140370008155292988479275', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46362214801544550403374400658', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0662554376171682, 'bad_primes': [2, 3], 'central_character': '128.109', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/2/v/a/109/27'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-384-128.109-c1-0-26', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-384-128.109-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7510726534376488, 'root_angle': 0.17638825773845054, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.31641331963299723725309191666', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2936402735009434353161054740141', 'Lhash_array': ['2936402735009434353161054740141'], 'label': '2-384-128.109-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/2/v/a/109/27'}